The normal distribution is a model distribution which many sets of data fall upon. It can be proven that the sums of draws from a box approaches normal distribution as the number of draws approaches infinity, no matter what is in the box (as long as there are at least two distinct values). The bell curve, or normal distribution curve, is a very useful model of perfect normal distribution. The formula for the bell curve is e^-x2/2 / sqrt(2 pi). The area under this distribution curve is one, and the mean, median, and mode all occur at 0, and the curve is symmetric around the y-axis. This curve has no integral--therefore it is necessary to use numerical integration or a table to find integrals.

Here is a table of integrals of the normal distribution from 0 to z:

 z   .00    .01    .02    .03    .04    .05    .06    .07    .08    .09
-------------------------------------------------------------------------
 .0| .0000  .0040  .0080  .0120  .0159  .0199  .0239  .0279  .0319  .0359
 .1| .0398  .0438  .0477  .0517  .0557  .0596  .0635  .0675  .0714  .0753 
 .2| .0792  .0832  .0871  .0909  .0948  .0987  .1026  .1064  .1102  .1141 
 .3| .1179  .1217  .1255  .1293  .1331  .1368  .1406  .1443  .1480  .1517 
 .4| .1554  .1591  .1627  .1664  .1700  .1736  .1772  .1808  .1844  .1879 
 .5| .1915  .1950  .1985  .2019  .2054  .2088  .2122  .2156  .2190  .2224 
 .6| .2257  .2291  .2324  .2356  .2389  .2421  .2454  .2486  .2517  .2549 
 .7| .2580  .2611  .2642  .2673  .2703  .2734  .2764  .2793  .2823  .2852 
 .8| .2881  .2910  .2939  .2967  .2995  .3023  .3051  .3078  .3106  .3133 
 .9| .3159  .3186  .3212  .3238  .3264  .3289  .3315  .3340  .3364  .3389 
1.0| .3413  .3437  .3461  .3485  .3508  .3531  .3554  .3577  .3599  .3621 
1.1| .3643  .3665  .3686  .3707  .3728  .3749  .3770  .3790  .3810  .3830 
1.2| .3849  .3868  .3888  .3906  .3925  .3943  .3962  .3979  .3997  .4015 
1.3| .4032  .4049  .4066  .4082  .4099  .4115  .4131  .4146  .4162  .4177 
1.4| .4192  .4207  .4222  .4236  .4251  .4265  .4278  .4292  .4306  .4319 
1.5| .4332  .4345  .4357  .4370  .4382  .4394  .4406  .4418  .4429  .4441 
1.6| .4452  .4463  .4474  .4484  .4495  .4505  .4515  .4525  .4535  .4545 
1.7| .4554  .4564  .4573  .4582  .4591  .4599  .4608  .4616  .4625  .4633 
1.8| .4641  .4648  .4656  .4664  .4671  .4678  .4685  .4692  .4699  .4706 
1.9| .4713  .4719  .4726  .4732  .4738  .4744  .4750  .4756  .4761  .4767 
2.0| .4772  .4778  .4783  .4788  .4793  .4798  .4803  .4808  .4812  .4817 
2.1| .4821  .4826  .4830  .4834  .4838  .4842  .4846  .4850  .4854  .4857 
2.2| .4861  .4864  .4868  .4871  .4874  .4878  .4881  .4884  .4887  .4890 
2.3| .4893  .4895  .4898  .4901  .4903  .4906  .4909  .4911  .4913  .4916 
2.4| .4918  .4920  .4922  .4924  .4926  .4928  .4930  .4932  .4934  .4936 
2.5| .4938  .4940  .4941  .4943  .4944  .4946  .4948  .4949  .4950  .4952 
2.6| .4953  .4955  .4956  .4957  .4958  .4960  .4961  .4962  .4963  .4964 
2.7| .4965  .4966  .4967  .4968  .4969  .4970  .4971  .4972  .4973  .4974 
2.8| .4974  .4975  .4976  .4977  .4977  .4978  .4979  .4979  .4980  .4981 
2.9| .4981  .4982  .4982  .4983  .4983  .4984  .4984  .4985  .4985  .4986 
3.0| .4986  .4987  .4987  .4988  .4988  .4988  .4989  .4989  .4990  .4990 
3.1| .4990  .4991  .4991  .4991  .4991  .4992  .4992  .4992  .4993  .4993 
3.2| .4993  .4993  .4993  .4994  .4994  .4994  .4994  .4995  .4995  .4995 
3.3| .4995  .4995  .4995  .4996  .4996  .4996  .4996  .4996  .4996  .4996 
3.4| .4997  .4997  .4997  .4997  .4997  .4997  .4997  .4997  .4997  .4997 
3.5| .4998  .4998  .4998  .4998  .4998  .4998  .4998  .4998  .4998  .4998 
3.6| .4998  .4998  .4998  .4998  .4999  .4999  .4999  .4999  .4999  .4999 
3.7| .4999  .4999  .4999  .4999  .4999  .4999  .4999  .4999  .4999  .4999 
3.8| .4999  .4999  .4999  .4999  .4999  .4999  .4999  .4999  .4999  .4999 
3.9|~.5000